To clear up something, you can die during the mission, but you cannot die in between the 25 precision kills. For example, you can die near the beginning of the mission, get your 25 kills, and still get your achievement. What you can't do is get 20 kills, then die, then get 5 more. You'd have to start over and get 25 more at that point.
See the video below for a great place to get this achievement early. Thanks to squareonegames for making the video!